The Hour as a Measure of Angle - and some random talking about science!

So going through high school geometry and trigonometry one learns about certain triangles with angles with particular properties. The angles of the 30-60-90 triangle and the 45-45-90 triangle all can have their trig functions expressed precisely and concisely using square roots. This makes these angles particularly useful, as one doesn't need a table or a calculator to work problems with these angles.Now, the greatest common divisor of these angles is fifteen degrees. Interestingly, fifteen degrees divides a full circle twenty four times, the same number as there are hours in a day (and in all probability is where the idea of dividing a day into twenty four hours comes from).

So I propose an alternate unit for angle measure, the "archour" by extension of the "arcminute" and "arcsecond", equal to fifteen degrees. This makes the friendly angles of 30, 45, 60, 90, 180, and 360 degrees relatively low integers when expressed in archours. Finer divisions will be standard decimal metric prefixes. This will be easier to learn for new mathematics students than the degree, with far too many useless angles, and the radian, with an irreducible irrational factor in all practical angles. For technical purposes the radian will be retained, but the degree will be phased out in favor of the easier to learn archour.

Naturally I expect uptake to be slow; Europe took a century to adopt metric, Britain took two, and the US still hasn't. This modest proposal is in the same vein, and I would like to hear feedback.

No we didn't, still buy milk and beer by the pint but petrol by the litre

Interesting points you made though.

145 Mods isn't too many. 9 types of copper and 8 types of tin aren't too many. 3 types of coffee though?I know that you believe that you understood what you think I said, but I am not sure you realise that what you read was not what I meant.

So going through high school geometry and trigonometry one learns about certain triangles with angles with particular properties. The angles of the 30-60-90 triangle and the 45-45-90 triangle all can have their trig functions expressed precisely and concisely using square roots. This makes these angles particularly useful, as one doesn't need a table or a calculator to work problems with these angles.Now, the greatest common divisor of these angles is fifteen degrees. Interestingly, fifteen degrees divides a full circle twenty four times, the same number as there are hours in a day (and in all probability is where the idea of dividing a day into twenty four hours comes from).

You do know that every single trig function can be expressed precisely ... the only issue being it's A LIMIT. Which means to get more accurate, you need to sum numbers ... infinitely.

So I propose an alternate unit for angle measure, the "archour" by extension of the "arcminute" and "arcsecond", equal to fifteen degrees. This makes the friendly angles of 30, 45, 60, 90, 180, and 360 degrees relatively low integers when expressed in archours. Finer divisions will be standard decimal metric prefixes. This will be easier to learn for new mathematics students than the degree, with far too many useless angles, and the radian, with an irreducible irrational factor in all practical angles. For technical purposes the radian will be retained, but the degree will be phased out in favor of the easier to learn archour.

What would you do of "angle's minutes/second" ? (they are 1/60 or 1/3600 of 1°).

Naturally I expect uptake to be slow; Europe took a century to adopt metric, Britain took two, and the US still hasn't.

That's because it's french. They do hate recognizing our system was better

BTW: Nobody uses angle anyway. Radians are much cooler, because 1 rad is a complete rotation, so it's much easier to express things such as rotation speed for a motor or something ... ^^. And this is also basically what you said with hours, assuming one hour equals to 1 grad ... AND plane pilots already use what you said I think

That's because it's french. They do hate recognizing our system was better

Try bribing the Americans with another tall statue since the Statue of Liberty has warn off. Remember since France was in NATO, Britain gave the USSR the jet engine

145 Mods isn't too many. 9 types of copper and 8 types of tin aren't too many. 3 types of coffee though?I know that you believe that you understood what you think I said, but I am not sure you realise that what you read was not what I meant.

Perhaps a better word than "precisely" is "concisely" - those angles require only a single term to have their trig functions expressed exactly. And if I remember correctly there are 2*pi radians in a rotation, not one.

Degrees, radians, and rotations are all measures of angle; I just feel the degree is the least graceful. Radians are extremely useful in mathematics and physics, as certain trig identities and other formulae only work when expressed in radians; in this manner radians are a sort of "natural" unit for angle. Rotations are also useful, but in different contexts, primarily engineering, where the important thing is not where on a circle one is located but how many times one has gone around it.

Degrees, however, are not as convenient or systematic, and the archour is intended to replace them with something easier to use for the times when we want part of a circle expressed as a rational number. One objective with this unit is to make the bridge between basic angle units (degree or archour) and radians easier for students. This shift is easier for archours because one archour (15 degrees) is pi/12 radians, two archours (30 degrees) is pi/6 radians, three archours (45 degrees) is pi/4 radians, four archours (60 degrees) is pi/3 radians, and six archours (90 degrees) is pi/2 radians - simple fractions of pi in radians, small integers in archours, and concise trig functions all around. The archour is the greatest common divisor of these common angles.

Perhaps a better word than "precisely" is "concisely" - those angles require only a single term to have their trig functions expressed exactly. And if I remember correctly there are 2*pi radians in a rotation, not one. True. Though to me it's so obvious than my brain assume the unit is "2Pi*radian" and not radian itself ^^.

Degrees, radians, and rotations are all measures of angle; I just feel the degree is the least graceful. Radians are extremely useful in mathematics and physics, as certain trig identities and other formulae only work when expressed in radians; in this manner radians are a sort of "natural" unit for angle. Rotations are also useful, but in different contexts, primarily engineering, where the important thing is not where on a circle one is located but how many times one has gone around it.

Degrees, however, are not as convenient or systematic, and the archour is intended to replace them with something easier to use for the times when we want part of a circle expressed as a rational number. One objective with this unit is to make the bridge between basic angle units (degree or archour) and radians easier for students. This shift is easier for archours because one archour (15 degrees) is pi/12 radians, two archours (30 degrees) is pi/6 radians, three archours (45 degrees) is pi/4 radians, four archours (60 degrees) is pi/3 radians, and six archours (90 degrees) is pi/2 radians - simple fractions of pi in radians, small integers in archours, and concise trig functions all around. The archour is the greatest common divisor of these common angles. Well, just assume degrees are 1/6 of a minute and you're done ... scalars aren't annoying, are they ? It's not like your using logarythmic scale for angles ...

With E = mc² you can also use Light as measurement of Mass. Light does have a Mass, even though it only consists out of the Movement Energy.

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Photons can't have mass because they wouldn't travel at the speed of light, to which, as fair as we know, it is experimental fact that they do.

M = mc²/(√1-(v/c)²) where M = mass at velocity

As v approaches c, (v/c)² approaches 1, and so (1 - (v/c)²) approaches zero. This in turn means M approaches infinity. E=mc² only applies to still objects, whereas E²=(mc²)²+(pc)² Applies to moving objects, and if it is moving at the speed of light it must have 0 mass.

E²=(0c²)²+(pc)²E²=0+(pc)²E=pc

The momentum of a photon is p = (ℎf)/c where ℎ = plancks constant and f = frequencyso E=c((ℎf)/c)so the energy of a photon is E=ℎf

What I SAID is that the Photons have the Mass of the Energy which is moving the Photon. Not that the Photons have Mass.

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What I SAID is that the Photons have the Mass of the Energy which is moving the Photon. Not that the Photons have Mass.

But it doesn't, since it takes no energy at all to move something with no mass to the speed of light (or any speed). When a photon hits something, it has a probability to either get absorbed (transferring its energy) or just bounce off.

It takes no Energy to accellerate it, that is why it can move at Lightspeed, duh! The Energy ITSELF has the Mass (Energy = MASS times Lightspeed squared), and since Photons evidently have Energy, they have indirect Mass, even if though are weightless themselves.

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I never said they have Mass by themselves, so why did you try to proove me wrong? I always said they have the mass of the ENERGY moving them, not that they have their own Mass.

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And Accelleration of Matter increases Mass, making the generic F = m * a wrong after exceeding about 10% Lightspeed, that results in Energy having a Mass by itself, what is also the reason why Light doesn't move instantaneous, but has an actual Limit. And it also results in Gravity affecting Light since the Energy moving the Light has a Mass as seen by Black Holes.

If Energy wouldn't have Mass, then the limit of Lightspeed wouldn't even exist and any Light would just move instant.

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Even then, in relativity, Gravity does not actually alter the direction of light at all but changes the space around it. According to the photon, it is still travelling in a straight line. I don't quite understand this part but the speed limit for light is set by time dilation, as the speed of light happens to be where time stops relative to the object at speed. Although it isn't "instantaneous", it is still counted as infinite because of this time dilation.